We present the first inelastic neutron scattering study of the short wavelength dynamics in a phospholipid bilayer. We show that inelastic neutron scattering using a triple-axis spectrometer at the high flux reactor of the ILL yields the necessary resolution and signal to determine the dynamics of model membranes. The results can quantitatively be compared to recent Molecular Dynamics simulations. Reflectivity, in-plane correlations and the corresponding dynamics can be measured simultaneously to gain a maximum amount of information. With this method, dispersion relations can be measured with a high energy resolution. Structure and dynamics in phospholipid bilayers, and the relation between them, can be studied on a molecular length scale.